Probalign is a sequence alignment tool that calculates a maximum expected accuracy alignment using partition function posterior probabilities.U. Roshan and D. R. Livesay, Probalign: multiple sequence alignment using partition function posterior probabilities, Bioinformatics, 22(22):2715-21, 2006 (PDF) Base pair probabilities are estimated using an estimate similar to the Boltzmann distribution. The partition function is calculated using a dynamic programming approach.
Algorithm The following describes the algorithm used by probalign to determine the base pair probabilities.Lecture "Bioinformatics II" at University of Freiburg
Alignment score To score an alignment of two sequences two things are needed: a similarity function (e.g. PAM, BLOSUM,...) affine gap penalty: The score of an alignment a is defined as:
Now the boltzmann weighted score of an alignment a is:
Where is a scaling factor.
The probability of an alignment assuming boltzmann distribution is given by
Where is the partition function, i.e. the sum of the boltzmann weights of all alignments.
Dynamic programming Let denote the partition function of the prefixes and . Three different cases are considered: the partition function of all alignments of the two prefixes that end in a match. the partition function of all alignments of the two prefixes that end in an insertion . the partition function of all alignments of the two prefixes that end in a deletion . Then we have:
Initialization The matrixes are initialized as follows:
Recursion The partition function for the alignments of two sequences and is given by , which can be recursively computed:
analogously
Base pair probability Finally the probability that positions and form a base pair is given by:
are the respective values for the recalculated with inversed base pair strings.
See also ProbCons Multiple Sequence Alignment
References
External links Probalign Webservice